The generator matrix

 1  0  1  1  1 3X+2  1  1 2X  1  1  1  1
 0  1 X+1 3X+2  3  1  2 X+1  1  1 X+3 2X 2X
 0  0 2X+2  0  2 2X 2X  0  2  2 2X 2X+2 2X+2
 0  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X

generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+46x^10+112x^11+633x^12+480x^13+612x^14+112x^15+45x^16+6x^18+1x^20

The gray image is a code over GF(2) with n=104, k=11 and d=40.
This code was found by Heurico 1.16 in -1.01e-007 seconds.